
\begin{tikzpicture}[scale=.9]
  \coordinate[label=above left:$O$] (O) at (0,0);
  \coordinate[label=above:$A$] (A) at (0,2);
  \coordinate[label=below:$C$] (C) at (0,-1);
  \coordinate[label=above:$B$] (B) at (4/3,0);
  \coordinate[label=below:$D$] (D) at (-4/5,0);
  \pic[mark angle={teal}{3mm}{1}] {right angle=B--O--A};
  \draw[thick] (A) -- (B) -- (C) -- (D) -- cycle;
  \draw (A) -- (C) (B) -- (D);
  \foreach \squno/\squl/\lpos/\squr/\rpos/\Ppos/\Qpos/\lcolor/\rcolor in {
      1/A/right/B/above/above/right/red/orange,
      2/B/below/C/right/below/below/orange/green,
      3/C/left/D/below/below/left/green/cyan,
      4/D/above/A/below/above/left/cyan/red} {
    \coordinate[label=\lpos:$\squl_\squno$]
      (\squl\squno) at ($ (\squr)!1! -90:(\squl) $);
    \coordinate[label=\rpos:$\squr_\squno$]
      (\squr\squno) at ($ (\squl)!1! 90:(\squr) $);
    \coordinate[label=\Ppos:$P_\squno$]
      (P\squno) at ($ (\squl)!(O)!(\squr) $);
    \coordinate[label=\Qpos:$Q_\squno$]
      (Q\squno) at ($ (\squl\squno)!(O)!(\squr\squno) $);
    \draw[thick, densely dash dot]
      (\squl) -- (\squr\squno) -- (\squl\squno) -- (\squr);
    \draw[densely dashed] (O) -- (Q\squno);
    \fill[opafill=\lcolor]
      (\squl) -- (\squr\squno) -- (Q\squno) -- (P\squno) -- cycle;
    \fill[opafill=\rcolor]
      (\squr) -- (\squl\squno) -- (Q\squno) -- (P\squno) -- cycle;
  }
  \path[name path=A1M] (A1) -- ($ (O)!(A1)!(A) $);
  \path[name path=P1Q1] (P1) -- (Q1);
  \path[name intersections={of=A1M and P1Q1}]
    coordinate[label=above:$M$] (M) at (intersection-1);
  \path[name path=C2N] (C2) -- ($ (O)!(C2)!(C) $);
  \path[name path=P2Q2] (P2) -- (Q2);
  \path[name intersections={of=C2N and P2Q2}]
    coordinate[label=above:$N$] (N) at (intersection-1);
  \coordinate[label=right:$L$] (L) at ($ (A1)!1/2!(C2) $);
  \draw[densely dash dot dot] (A1) -- (C2)
    (A1) -- (M) (C2) -- (N) (B) -- (L);
  \fill[opafill=yellow] (O) -- (B) -- (A1) -- (M) -- cycle
    (O) -- (B) -- (C2) -- (N) -- cycle;
  \fill[opafill=pink] (A) -- (B) -- (C) -- cycle
    (A1) -- (B) -- (C2) -- cycle;
\end{tikzpicture}
